Distribution Definition and 1000 Threads

If the normalized probability density of the normal distribution is ## p(x) = \frac {1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}} ##, then if ##\sigma = 0.0001## and in the special case ## x = \mu##, wouldn't the probability density at this point, ##p(\mu)##, exceed 1 since it is equal...

Homework Statement Hi, I have the probabilty density: ##p_{n}=(1-p)^{n}p , n=0,1,2... ## and I am asked to find the characteristic function: ##p(k)= <e^{ikn}> ## and then use this to determine the mean and variance of the distribution. Homework Equations [/B] I have the general expression...

I have calculated characteristic function of normal distribution f_{X}(k)=e^{(ika-\frac{\sigma ^{2}k^{2}}{2})} and now I would like to find the moments, so I know that you could expand characteristic function by Taylor series f_{X}(k)=exp(1+\frac{1}{1!}(ika -...

Hello, guys. I am trying to solve for characteristic function of normal distribution and I've got to the point where some manipulation has been made with the term in integrands exponent. And a new term of t2σ2/2 has appeared. Could you be so kind and explain that to me, please...

Hello Everyone Hope you will be fine I am trying to estimate assembly wise power distribution of pwr core. Can anyone let me know if F7 tally correspond directly to power distribution or else i need some additional calculations?

In a digital communication channel, assume that the number of bits received in error can be modeled by a binomial random variable, and assumed that a bit is received in error is 1×〖10〗^(−5) . if 16 million bits are transmitted, What is the probability that more than 150 errors occur? Find the...

Assuming that the number of marks scored by a candidate is normally distributed, find the mean and the standard deviation, if the number of first class students(60% or more marks) is 25, the number of failed students(less than 30%marks) is 90 and the total number of candidates appearing for the...

I'm trying to figure out why my back hurts when I sleep and I can't figure out the physics behind it. So I sleep on an air mattress. The mattress fits firmly into the frame, which puts a constraint on the mattress to where it cannot expand on it's sides. Think of the mattress as being in a box...

Homework Statement On average, 2 students per hour come into the class. What is the probability that the time between two consecutive arrivals is in the interval <10 minutes; 50 minutes>. Homework Equations p(k)=P(Y=k)=((lambda*t)k*(e-lambda*t)/k! The Attempt at a Solution I've tried using...

Hey all, So the question in Jackson 1.4 is that I have 3 spheres that all have a total charge Q on them, but each sphere has different material properties. For instance, I have a conducting sphere, a sphere with a uniform charge distribution, and one with a charge distribution that has a...

Hi everyone. I've been considering switching out of using a Windows laptop in favour of Linux. What I'm curious of is do any of you here on PF use the Linux OS. If so, which distribution do you use (Ubuntu, Fedora, etc.)? What has been your experience using Linux? Appreciate any insights any of...

Homework Statement find the average energy of a system with n energy states (0, 1E, 2E, 3E...nE) Homework Equations P(E) = e-BE/Z - where B=1/KbT and Z= ∑e(-BE)n <E>=∑(nE* (e-BE)n) /Z The Attempt at a Solution i feel like I've gone down the correct path - that is finding result of the sums. Z...

Homework Statement An initial particle distribution n(r, t) is distributed along an infinite line along the z-axis in a coordinate system. The particle distribution is let go and spreads out from this line. a) How likely is it to find a particle on a circle with distance r from the z-axis at...

Homework Statement Hi everybody! I'm very stuck trying to solve this problem, hopefully some of you can give me a clue about in which direction I should go: Determine the multipole expansion in two dimensions of the potential of a localized charge distribution ##\lambda(\vec{x})## until the...

Homework Statement A barbershop has two barbers: an experienced owner and an apprentice. The owner cuts hair at the rate of 4 customers/hour, while the apprentice can only do 2 customers/hour. The owner and the apprentice work simultaneously, however any new customer will always go first to the...

The question asks: A physical device can be in three states: A,B,C. The device operates as follows (all time units are in hours): The device spends an exponentially distributed amount of time in stateAA (with mean of 12minutes) and then with probability 0.6 goes to state B, and with...

So the problem asks: A computer server runs smoothly for Exp(0.2) days and then takes Exp(0.5)days to fix. The server is running fine on Monday morning, t=0. Find the probability that the server was fixed at least once (i.e. at least one complete repair was done) in the next 7 days and the...

This is my first time using this site so please excuse me if I missed any guidelines. 1. Homework Statement A plastic rod having a uniformly distributed charge Q=-25.6pC has been bent into a circular arc of radius R=3.71cm and central angle ∅=120°. With V=0 at infinity, what is the electric...

Maxwellian velocity distribution is obtained by $$g(v_x)\propto e^{-mv_x^2/2k_B T}$$ and when extended to 3 dimensions the distribution becomes: $$\propto e^{-mv_x^2/2k_B T}e^{-mv_y^2/2k_B T}e^{-mv_z^2/2k_B T} = e^{-mv^2/2k_B T}$$ Now looking at the speed distribution we take a spherical shell...

Homework Statement I am told that the gravitational force of a mass m located inside an isotropic distribution of spherical radius R and total mass M is given by Fg = -GmM(r)/r^2 where r is the distance between m and the center of distribution and M (r) is the mass contained below the distance...

Hello PF, I am trying to analyze a a beam, connected to another beam at one side at multiple locations (bad quality drawing below). The top side of the beam extends further and sit on another beam, while the shorter lower side is directly connected to another beam. They are all bolted...

Homework Statement The average lifetime of muons at rest is τμ0 = 2.2 μs. A laboratory measurement on the decay in flight of muons in a beam emerging from a particle accelerator yields an average lifetime of τμ = 6.6 μs, as measured in the lab frame Σ. (g) [3 points] Given a large ensemble of...

I am doing a project for a course and it asks me to draw annotated drawings of the distribution network including generators, transmission systems, distribution system and low voltage loads which in general is all fine. However, I have come across a question that asks me to draw an annotated...

Homework Statement Gas particles of a particular gas have a speed distribution function of fv = Cv/(v2 +vo2)2 a. Find the value of C b. Calculate the most probable speed c. What fractions of the particles are moving faster than the most probable speed Homework EquationsThe Attempt at a...

Hi guys, I have a question about computing conditional probabilities of a Poisson distribution. Say we have a Poisson distribution P(X = x) = e^(−λ)(λx)/(x!) where X is some event. My question is how would we compute P(X > x1 | X > x2), or more specifically P(X> x1 ∩ X > x2) with x1 > x2? I...

Is the distribution the same as Boltzmann distribution? Have anyone made a mathematic equation for the KE of free electrons on a piece of metal?

Hello, I have a question about Boltzmann Distribution. I wonder why partial N of Nj is 1 and partial U of Nj=Ej. because N is constant, partial N of Nj has to be 0 and Partial Nj of U has to be 0 as well. They are constants so, to make sense of the equation, alpha and beta have to be 0 but...

please am new here and i need a help, i can use poisson distribution to get a probability but how can i use it to get several outcome? like over and under ,1x2? thanks

Hey guys, I am building a small water ramp that will extend from a dock and into the water with a buoy at the end. I could probably just use trial and error, but thought it would be fun to make some rough calculations to help my design. This picture (http://imgur.com/a/bHYfG) shows the...

Is this a ground breaking observation or does it agree with other observations? atures and the Wing-Ford band, presented in a recent paper. arXiv:1610.03854 [pdf, ps, other] The observed spatial distribution of matter on scales ranging from 100kpc to 1Gpc is inconsistent with the standard...

Hello everybody, - In quantum mechanics, the state ## | \psi \rangle ## of a system that is in thermodynamic equilibrium can be expressed as a linear combination of its stationary states ## | \phi _n \rangle ## : $$ | \psi \rangle = \sum_n c_n | \phi _n \rangle $$ It permit us to express the...

I'm looking for the inverse functions of the Maxwell-Boltzmann distribution and Planck's Law. Planck's Law in terms of the wavelength. Any of you know of any literature on this topic?

Homework Statement Consider helium as ideal gas with a Maxwell distribution of speeds. (a) Investigate the maximal value Fmax at the peak of the Maxwell distribution F(v): Calculate this value for He at T = 300 K and at 600 K, and for N2 at 300 K b) For He at 300 K, obtain speeds v1...

Hello. Given a range of time in which an event can occur an indefinite number of times, we say a random variable X folows a poisson distribution when it follows this statements: X is the number of times an event occurs in an interval and X can take values 0, 1, 2, … The occurrence of one event...

Homework Statement The Lorentz Distribution is given by p(x) = \frac{1}{pi}\frac{ϒ}{(x-a)^2+ϒ^2} for -∞≤x≤∞. a) Sketch the distribution for a=0, ϒ=1, and compare the form to the Gaussian Distribution. b) Calculate the first moment of the distribution assuming again that a =0 and ϒ =1. c)...

Homework Statement A good hitter in baseball has a batting average of .300 which means that the hitter will be successful three times out of 10 tries on average. Assume that the batter has four times at bat per game.a) What is the probability that he will get two hits or less in a three game...

Homework Statement Hi everybody! I'm preparing for an exam of electromagnetism, and I am struggling with the last question of this problem (hopefully the two first ones are correctly solved): Given potential: ##\phi(\vec{r}) = k \frac{q}{r} e^{-r/R}## with ##r=\sqrt{x^2 + y^2 + z^2}## and ##R...

Hi, I have quite a superficial understanding of Droop control: http://www.openelectrical.org/wiki/index.php?title=Droop_Control https://en.wikipedia.org/wiki/Droop_speed_control I'm not after a super technically detailed explanation, but if anyone has any more detailed sources for how it is...

<<Mentor note: Moved from this thread>> I read this article http://thedaily.case.edu/rotating-galaxies-distribution-normal-matter-precisely-determines-gravitational-acceleration/ It claims that the rotation of galaxies can be explained without a need for dark matter. I not an educated...

My undergrad probability theory course just got to random variables and distribution functions. Up until this point, the material was very straightforward and I could understand what was being done, but I feel that I am just not seeing the jump between probability with sets and probability with...

Hi, I have a question about Maxwell-Boltzmann Distribution. First, because of mass conservataion and energy conservatioin, Sum Ni and Sum EiNi must be constant. Partial of both sum will be 0. Is that why we adopted constant alpha as a parametric constant? because without alpha, partial Nj of...

Homework Statement Consider the charge distribution of a uniformly charged ring of radius ##R## and charge ##Q## at a distance ##d## above the origin and a uniformly charged ring of radius ##R## and charge ##-Q## at a distance ##d## below the origin. (a) Calculate the dipole moment of this...

Homework Statement Homework Equations Work = - (integral of) (E dot dl) The Attempt at a Solution Hi, I know that the right answer is D zero, but I fail to understand why. I said that the answer was A as I have different charges, and I thought that depending on how I approach each...

The problem I am trying to show that ##a'c' \vee c'd \vee ab'd ## is equivalent to ## (a \vee c')(b' \vee c')(a' \vee d) ## The attempt ## (a \vee c')(b' \vee c')(a' \vee d) \\ (c' \vee (ab'))(a' \vee d)## The following step is the step I am unsure about. I am distributing the left...

Three conditions must be met in order for the Poisson Distribution to be used: 1) The average count rate is constant over time 2) The counts occurring are independent 3) The probability of 2 or more counts occurring in the interval $n$ is zero Simply, why must these conditions be met for valid...

41 35 29 43 16 49 32 6 20 10 26 28 47 43 7 36 13 10 0 2 The data represent the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the...

Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 547 and standard deviation 85. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 21.3 and...

If an observer accelerates through a simple vacuum, it is often said that they see Unruh radiation with acceleration of ##2.5*10^{20} m/s^2## equivalent to a temperature of 1K, but I haven't seen the polar distribution described, one might assume it was from 'ahead' of the direction of...

Homework Statement Please help! I'm new to Gaussian and I've been on this problem for hours, I can't crack it at all (no pun intended) can anyone provide a detailed walk through the answers? On average 5% of eggs contain a hereditary condition. Use Gaussian distribution to find the...

Homework Statement I am trying to calculate the power of Rload in the circuit attached (SEE ATTACHED CIRCUIT). The coupler I am trying to model is the Agilent 778D. Can someone verify that I calculate this out correctly? Homework Equations y dB = 10 * log10(x) V = i * R P = v * i The Attempt...